Question

Write a two-column proof. Given: MS ≅ RQ, MS || RQ Prove: Δ M S P ≅Δ R Q P

Answer 1

We can conclude that ΔMSP ≅ ΔRQP under SAS conditions.

What do we mean by a triangle's congruency?

• If all three corresponding sides and angles of two triangles are the same size, they are said to be congruent.
• These triangles can be moved, rotated, flipped, and turned to appear identical.
• If they are moved, they will coincide.
• When two triangles satisfy the five congruence conditions, congruence exists.
• They are the side-side-side (SSS), side-angle-side (SAS), angle-side-angle (ASA), angle-angle-side (AAS), and right angle-hypotenuse-side (RHS).

So,

Given: MS ≅ RQ, MS || RQ

To Prove: ΔMSP ≅ ΔRQP

• MS = RQ = (Given)
• SP = PQ = (Q is the midpoint)
• So, ∠MSP = ∠RQP (SAS)

ΔMSP ≅ ΔRQP is proved.

Therefore, ΔMSP ≅ ΔRQP under SAS condition.

Know more about the congruency of a triangle here:

brainly.com/question/2938476

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